Deep learning semantic segmentation methods have shown promising performance for very high 1-m resolution land cover classification, but the challenge of collecting large volumes of representative training data creates a significant barrier to widespread adoption of such models for meter-scale land cover mapping over large areas. In this study, we present a novel label-efficient approach for statewide 1-m land cover classification using only 1,000 annotated reference image patches with self-supervised deep learning. We use the "Bootstrap Your Own Latent" pre-training strategy with a large amount of unlabeled color-infrared aerial images (377,921 patches of 256x256 pixels at 1-m resolution) to pre-train a ResNet-101 convolutional encoder. The learned encoder weights were subsequently transferred into multiple deep semantic segmentation architectures (FCN, U-Net, Attention U-Net, DeepLabV3+, UPerNet, PAN), which were then fine-tuned using very small training dataset sizes with cross-validation (250, 500, 750 patches). Among the fine-tuned models, we obtained 87.14% overall accuracy and 75.58% macro F1 score using an ensemble of the best-performing U-Net models for comprehensive 1-m, 8-class land cover mapping, covering more than 123 billion pixels over the state of Mississippi, USA. Detailed qualitative and quantitative analysis revealed accurate mapping of open water and forested areas, while highlighting challenges in accurate delineation between cropland, herbaceous, and barren land cover types. These results show that self-supervised learning is an effective strategy for reducing the need for large volumes of manually annotated data, directly addressing a major limitation to high spatial resolution land cover mapping at scale.